"We have looked at this thing from every which way," Thomas told the insider newsletter. "It doesn't make sense to get in. We don't see a chance to win. I don't want to be a second candidate against an incumbent."
His decision means Mourdock will likely have a clear shot against Lugar in the May primary. The state filing deadline is Feb. 21.
Thomas also said he would not endorse Lugar or Mourdock.
In 2010, Thomas spent $600,000 out of his own pocket to challenge then-Rep. Mark Souder (R-Ind.). Thomas lost his primary bid to Souder by about 14 points in what was a crowded GOP field.
Rep. Elijah Cummings, D-Md., right, hugs Harold Schaitberger, General President of the International Association of Fire Fighters, after the Congressman spoke at the IAFF's Legislative Conference General Session at the Hyatt Regency on Capitol Hill, March 9, 2015. The day featured addresses by members of Congress and Vice President Joe Biden.